I got a new job as an engineer. My previous job was not engineering related. Anyhow, my previous boss wrote me a recommendation letter due to my outstanding performance. Do you recommend I send this recommendation letter to my new manager so he gets to know more about how I value a job or a task at hand regradless if it's engineering or not? Thank you for your help in advance.
I don't think you can gain much by doing so. You already got the job, promises and agreements already have been made, now it's time to deliver.
I would however recommend to attach it to your resume/CV on application to next job even if it's not engineer-related. Good recommendation letter is not something everybody has, and there is a time and place to submit it.
Congratulations on your job!
IMO, I would trot out the rec letter ONLY_IF it highlighted some kind of marketable skill set that you could then demonstrate is laterally transferable from the industry that previously employed you to the current and ONLY_IF that particular skill set was what the new job was seeking. e.g. Engineers aren't exactly known for their effervescing, outgoing personalities, generally speaking, but if you were seeking a position as an engineer, and that position required client-facing skills, you will then want to mention how you developed a penchant for verbal tact and diplomacy skills with clients. And lookee here, Mr./Ms. Interviewer, I even have proof of concept right here from Mr. Former Employer attesting to it.